I wrote an article about this same general topic way back in 2007[1], wherein I conducted a thought experiment with an Arecibo observatory traveling away from Earth. I calculated that even mighty Arecibo would be unable to detect Earth's omnidirectional FM radio as far out as Saturn, let alone from another star.

Since that writing, we've lost Arecibo observatory, discovered gobs of exoplanets, started scrutinizing those exoplanets with JWST, and increased our radio sphere radius by another 19 lightyears.

[1] https://www.damninteresting.com/space-radio-more-static-less...